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1914] HIGH OEDER TO THE WHISPERING GALLERY 219
In the case of ordinary gases p/<r — fj?. As an example, take p = cosh (3 = 1'B; then (42) gives
1- -581W-1 e--SBn. ...........................(43) '
When n rises beyond 10, the damping according to (43) becomes small; and when n is at all large, the vibrations have very great persistence.
In the derivation of (42) we have spoken of stationary vibrations. But the damping is, of course, the same for vibrations which progress round the circumference, since these may be regarded as compounded of two sets of stationary vibrations which differ in phase by 90°.
Calculation thus confirms the expectation that the whispering gallery effect does not require a perfectly reflecting wall, but that the main features are reproduced in transparent media, provided that the velocity of waves is moderately larger outside than inside the surface of transition. And further, the less the curvature of this surface, the smaller is the refractive index (greater than unity) which suffices.ishes when n is made infinite, while the second and third parts compensate one another in virtue of (33). Accordingly (32) gives with regard to (34)